Abstract
In engineering applications almost all processes are described with the help of models. Especially forming machines heavily rely on mathematical models for control and condition monitoring. Inaccuracies during the modeling, manufacturing and assembly of these machines induce model uncertainty which impairs the controller’s performance. In this paper we propose an approach to identify model uncertainty using parameter identification, optimal design of experiments and hypothesis testing. The experimental setup is characterized by optimal sensor positions such that specific model parameters can be determined with minimal variance. This allows for the computation of confidence regions in which the real parameters or the parameter estimates from different test sets have to lie. We claim that inconsistencies in the estimated parameter values, considering their approximated confidence ellipsoids as well, cannot be explained by data uncertainty but are indicators of model uncertainty. The proposed method is demonstrated using a component of the 3D Servo Press, a multi-technology forming machine that combines spindles with eccentric servo drives.
Highlights
In science, technology and economics mathematical models are commonly used to describe physical phenomena, to solve design problems and to manage production processes
In this paper we propose an algorithm to detect model uncertainty using parameter identification, the optimal design of experiments approach and statistical hypothesis testing
In this paper we have seen how model uncertainty can be identified by combining the optimal design of experiments approach with parameter identification and statistical testing
Summary
Technology and economics mathematical models are commonly used to describe physical phenomena, to solve design problems and to manage production processes. This can be done using the methodology from optimal design of experiments, i.e., by deciding which sensors are best suited for gathering data in order to minimize the posterior variance of the estimated parameters Using these kinds of sensors and their optimal positions, measurements with maximum informational value can be obtained. To determine model uncertainty based on measurements obtained from an optimally designed experiment, we split the experimental data into a calibration and a validation set. In this work we discuss the same question but from a probabilistic frequentist point of view without any assumptions on the prior distribution of the parameters Another important approach to identify and control model uncertainty was introduced by Kennedy and O’Hagan (2001).
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